Name: 

Eve can choose from the following notebooks:
• lined pages come in red, green, blue, and purple
• graph paper comes in orange and black

If Eve needs one lined notebook and one with graph paper, which of the following pairs is not a possible outcome?

Evaluate.
8! + 1!

Evaluate.
(3!)²

Evaluate.

Solve for n, where n Î I.

Solve for n, where n Î I.

Solve for n, where n Î I.

Solve for n, where n Î I.

Evaluate.
₂₁P₂

Suppose a word is any string of letters. How many five-letter words can you make from the letters in KELOWNA if you do not repeat any letters in the word?

Suppose a word is any string of letters. How many two-letter words can you make from the letters in LETHBRIDGE if you do not repeat any letters in the word?

How many ways can 8 friends stand in a row for a photograph if Molly, Krysta, and Simone always stand together?

Indicate whether the Fundamental Counting Principle applies to this situation:
Counting the number of possibilities when picking a chair and a vice chair from a list of committee members.

A band sells shirts and CDs at their concerts. They have 3 CDs and there are 4 different styles of shirt available in small, medium, large, and extra large.
How many ways could you buy one CD and one shirt if you only consider one size of shirt?

A band sells shirts and CDs at their concerts. They have 3 CDs and there are 4 different styles of shirt available in small, medium, large, and extra large.
How many ways could someone buy two different CDs and a shirt?

A combination lock opens with the correct three-letter code. Each wheel rotates through the letters A to O. Suppose each letter can be used only once in a code. How many different codes are possible when repetition is not allowed?

The “Pita Patrol” offers these choices for each sandwich:
• white or whole wheat pitas
• 3 types of cheese
• 5 types of filling
• 12 different toppings
• 4 types of sauce

How many different pitas can be made with 1 cheese, 1 filling, 1 topping, and no sauce?

The “Pita Patrol” offers these choices for each sandwich:
• white or whole wheat pitas
• 3 types of cheese
• 5 types of filling
• 12 different toppings
• 4 types of sauce

How many different pitas can be made with 1 cheese, 1 filling, 1 topping, and 1 sauce?

A theatre is showing 3 action movies, 4 comedies, 4 dramas, and 1 foreign film. How many choices does Sophia have if she does not want to watch a drama or the foreign film?

A theatre is showing 2 action movies, 3 comedies, 3 dramas, 2 horror movies, and 2 foreign films. How many choices does Sophia have if she does not want to watch an action movie or a horror movie?

The numbers 1 to 20 are written on slips of paper and put in a hat. How many possible ways can you draw a either a number less than 5 or a perfect square from the hat?

Evaluate.
11 × 10 × 9!

Evaluate.

Evaluate.

Write the following expression using factorial notation.
7 × 6 × 5 × 4 × 3 × 2

How many ways can you arrange the letters in the word FACTOR?

Evaluate.
₅P₃

Evaluate.
₁₀₀P₁

There are nine different marbles in a bag. Suppose you reach in and draw one at a time, and do this three times. How many ways can you draw the three marbles if you do not replace the marble each time?

There are twelve different marbles in a bag. Suppose you reach in and draw two marbles one at a time without replacement. How many ways can you draw the two marbles?

Solve for r.
₃₄P_r = 34

Hannah plays on a local hockey team. The hockey uniform has:
• four different sweaters: white, blue, grey, and black, and
• two different pants: blue and grey.
a) Draw a tree diagram to determine how many different variations of the uniform the coach can choose from for each game are possible.
b) Confirm your answer to part a) using the Fundamental Counting Principle.

A combination lock opens with the correct four-digit code. Each wheel rotates through the digits 1 to 8.

a) How many different four-digit codes are possible?
b) Suppose each number can be used only once in a code. How many different codes are possible when repetition is not allowed?

Euchre is played with a deck of 24 cards that is similar to a standard deck of 52 playing cards, but with only the ace, 9, 10, jack, queen, and king for all four suits.
a) Count the number of possibilities of drawing a single card from a euchre deck and getting either a face card or a red card.
b) Does the Fundamental Counting Principle apply to this situation? Explain.

Evaluate the following. Show your work.

Consider the word PERMUTE and all the ways you can arrange its letter using each letter only once if the first letter is E.
a) One possible permutation is EPRETUM. Write three other possible permutations.
b) Use factorial notation to represent the total number permutations possible. Explain why your expression makes sense.

Which value is greater? Show your work.
A.               B.

At a used car lot, 6 different car models are to be parked close to the street for easy viewing. The lot has 3 red cars and 8 silver cars for the display. How many ways can the 6 cars be parked, if 2 red cars must be parked at either end of a row of 4 silver cars? Show your work.

An isogram is a word or phrase without a repeating letter.
Vito and Kira are playing a guessing game involving isograms. Vito thinks of a word with no repeated letters. He tells Kira that his word can be used to make 42 letter pairs. He gives LS, OG, and GO as examples.
a) How many letters are in Vito’s word?
b) What could Vito’s word be?

Kathy stacks 13 coins: 3 identical pennies, 4 identical nickels, 4 identical quarters, and 2 identical dimes. How many different ways can Kathy stack the coins in a single tower in each situation below. Show your work.
a) There are no conditions.
b) There must be a quarter on top and a quarter on the bottom.

Garrick stacks 15 coins: 9 identical pennies, 5 identical nickels, and 1 quarter. How many different ways can Garrick stack the coins in a single tower in each situation below. Show your work.
a) There are no conditions.
b) There must be a penny on top.

Compare the number of different arrangements you can make using all the letters in the words NANAIMO and FANNY BAY. Show your work.

Compare the number of different arrangements you can make using all the letters in the words RED DEER and REGINA. Show your work.

From a group of seven students, four students need to be chosen for a graduation committee.
a) How many committees are possible? Show your work.
b) How many committees are possible, if only three students are needed on the committee?
c) Compare your answers for parts a) and b). What do you notice? Explain why this occurred.

There are 12 boys and 15 girls in an English classroom. A group of 5 students is needed to read from a play. If there are 2 roles for boys, 2 roles for girls, and a narrator who could be a boy or a girl, how many different groups of 5 students are possible? Show your work.

There are 6 boys and 18 girls in a class. A group of 5 students is needed to work on a project. If at least 2 boys are needed, how many different groups of 5 students are possible? Show your work.

A hockey team is lining up in a row for a group photo. There team has 1 goalie, 4 defense, and 7 forwards. The photographer wants the defense on one side of the goalie and the forwards on the other side. How many ways can the team stand in a row for this pose? Show your work.

A hockey team is preparing for a group photo. The team has 2 goalie, 6 defense, and 8 forwards. The photographer wants two rows of eight players. How many ways can the team arrange eight players in the front row with at least one goalie? Show your work.

Twelve camp counselors are signing up for training courses that have only a limited number of spaces. Only 5 people can take the water safety course, 3 people can take the first aid course, 2 people can take the conflict management course, and 2 people can take the astronomy course. How many ways can the 12 counselors be placed in the four courses? Show your work.

Three vehicles are taking a choir of 25 students to a recital. A minibus can take 16 students, an SUV can take 6 students, and the remaining 3 students can ride with the choirmaster. How many ways can the 20 students be assigned to the 3 vehicles? Show your work.

How many different five-card hands that contain at most two face cards (jack, queen, or king) can be dealt to one person from a standard deck of playing cards? Show your work.